Explosion en temps fini pour l’équation de Schrödinger non linéaire stochastique surcritique

Anne de Bouard[1]; Arnaud Debussche[2]

  • [1] laboratoire de Mathématiques, Bât. 425, 91405 ORSAY CEDEX, FRANCE
  • [2] ENS de Cachan, Antenne de Bretagne, Campus de Ker Lann, Av. R. Schuman, 35170 BRUZ, FRANCE

Séminaire Équations aux dérivées partielles (2002-2003)

  • Volume: 2002-2003, page 1-14

How to cite

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de Bouard, Anne, and Debussche, Arnaud. "Explosion en temps fini pour l’équation de Schrödinger non linéaire stochastique surcritique." Séminaire Équations aux dérivées partielles 2002-2003 (2002-2003): 1-14. <http://eudml.org/doc/11073>.

@article{deBouard2002-2003,
affiliation = {laboratoire de Mathématiques, Bât. 425, 91405 ORSAY CEDEX, FRANCE; ENS de Cachan, Antenne de Bretagne, Campus de Ker Lann, Av. R. Schuman, 35170 BRUZ, FRANCE},
author = {de Bouard, Anne, Debussche, Arnaud},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-14},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Explosion en temps fini pour l’équation de Schrödinger non linéaire stochastique surcritique},
url = {http://eudml.org/doc/11073},
volume = {2002-2003},
year = {2002-2003},
}

TY - JOUR
AU - de Bouard, Anne
AU - Debussche, Arnaud
TI - Explosion en temps fini pour l’équation de Schrödinger non linéaire stochastique surcritique
JO - Séminaire Équations aux dérivées partielles
PY - 2002-2003
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2002-2003
SP - 1
EP - 14
LA - eng
UR - http://eudml.org/doc/11073
ER -

References

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  2. Bang, O.; Christiansen, P.L.; If, F.; Rasmussen K.O.; Gaididei, Y.B. White Noise in the Two-dimensional Nonlinear Schrödinger Equation. Appl. Anal. 1995, 57, 3–15. Zbl0842.35111MR1382938
  3. Da Prato, G.; Zabczyk, J. Stochastic Equations in Infinite Dimensions; Encyclopedia of Mathematics and its Applications, Cambridge University Press: Cambridge, England, 1992. Zbl0761.60052MR1207136
  4. de Bouard, A.; Debussche, A. A stochastic nonlinear Schrödinger equation with multiplicative noise. Comm. Math. Phys. 1999, 205, 161–181. Zbl0952.60061MR1706888
  5. de Bouard, A.; Debussche, A. The stochastic nonlinear Schrödinger equation in H 1 , Stochastic Analysis and Appl. 2003, 21, 97–126. Zbl1027.60065MR1954077
  6. de Bouard, A.; Debussche, A. On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation, Prob. Theory and Rel. Fields, 2002, 123, 76-96. Zbl1008.35074MR1906438
  7. de Bouard, A.; Debussche, A. Blow-up for the stochastic nonlinear Schrödinger equation with multiplicative noise, Preprint. Zbl1068.35191
  8. Debussche, A.; Di Menza L. Numerical simulation of focusing stochastic nonlinear Schrödinger equations. Phys. D 2002, 162, 131-154. Zbl0988.35156MR1886808
  9. Konotop, V.; Vázquez L. Nonlinear random waves; World Scientific Publishing Co., Inc.: River Edge, N.J., 1994. Zbl1058.76500MR1425880
  10. Millet, A.; Sanz-Solé, M. A simple proof of the support theorem for diffusion processes, Séminaire de Probabilité XXVIII, J. Azéma et al. ed., LNM 1583, 1994, 36-48. Zbl0807.60073MR1329099
  11. Sulem, C.; Sulem, P.L. The nonlinear Schrödinger Equation, Self-Focusing and Wave Collapse; Appl. Math. Sciences, Springer Verlag, New York, 1999. Zbl0928.35157MR1696311
  12. Ueda, T.; Kath W.L. Dynamics of optical pulses in randomly birefrengent fibers. Physica D 1992, 55, 166–181. Zbl0741.35082

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